Untangling Universality and Dispelling Myths in Mean-Variance Optimization

Abstract

Following Markowitz's pioneering work on mean-variance optimization (MVO), such approaches have permeated nearly every facet of quantitative finance. In the first part of the article, the authors argue that their widespread adoption can be attributed to the universality of the mean-variance paradigm, wherein the maximum expected utility and mean-variance allocations coincide for a broad range of distributional assumptions of asset returns. Subsequently, they introduce a formal definition of mean-variance equivalence and present a novel and comprehensive characterization of distributions, termed mean-variance-equivalent (MVE) distributions, wherein expected utility maximization and the solution of an MVO problem are the same. In the second part of the article, the authors address common myths associated with MVO. These myths include the misconception that MVO necessitates normally distributed asset returns, the belief that it is unsuitable for cases with asymmetric return distributions, the notion that it maximizes errors, and the perception that it underperforms a simple 1/n portfolio in out-of-sample tests. Furthermore, they address misunderstandings regarding MVO's ability to handle signals across different time horizons, its treatment of transaction costs, its applicability to intraday and high-frequency trading, and whether quadratic utility accurately represents investor preferences.